The Brewers have won four straight Cactus League games.
Davis' homer came only a few moments after the D-backs stole a 3-2 lead against Brewers pitching prospect Taylor Jungmann, who issued a two-out walk to Rossmel Perez and surrendered a single to Josh Wilson. When the runners broke for a double steal, neither the Brewers shortstop nor second baseman covered second base, and catcher Adam Weisenburger's throw sailed into center field for a run-scoring error.
The game's only other runs scored in the third inning, when Arizona's Eric Chavez and Milwaukee's Alex Gonzalez each hit two-run home runs.
Brewers starter Mark Rogers walked three batters and surrendered three hits including the Chavez home run, but was not charged with an earned run. Rogers was able to escape a bases-loaded, one-out jam in the first inning with the scoreless tie intact, and Chavez's home run in the third came with two outs, after an error charged to Brewers second baseman Scooter Gennett.
"We're getting there," Rogers said.
Rogers was taken off the hook for a loss in the bottom of the third inning, when the Brewers tied the game at 2 against Arizona reliever Joe Paterson. He followed D-backs starter Wade Miley, who walked two batters but did not allow a hit and logged two strikeouts in two scoreless innings.
It was a marked improvement from five days earlier, when Miley surrendered three runs on three hits in two innings of a loss to the Rangers.
"I was excited about getting back on the mound again and kind of have a positive outing coming off of last week," Miley said. "I located a whole lot better, like more down in the zone."
Brewers up next: Right-hander Tyler Thornburg will take the mound when the Brewers host the Rangers at Maryvale Baseball Park on Friday, with Thornburg's first pitch scheduled for 2:05 p.m. CT, weather permitting. He has allowed two runs on two hits in two innings in each of his two Cactus League starts, and walked three batters last time out in a win over the Angels. The Brewers should have right fielder Norichika Aoki and second baseman Rickie Weeks back in the lineup after they took Thursday off.
Adam McCalvy is a reporter for MLB.com. Read his blog, Brew Beat, and follow him on Twitter at @AdamMcCalvy. This story was not subject to the approval of Major League Baseball or its clubs.